If I pay my property taxes twice within the same calendar year (say Jan 2021 (for 2020) and Dec 2021 (for 2021)), can I deduct them both when I do my taxes for 2021 next year?
Yes, you can deduct the property taxes you actually pay in the tax year. It does not matter what year these taxes are for.
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Presuming, of course, that you don’t deduct them also in 2020. You deduct the taxes when actually paid, regardless of what year they were for.